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電気化学

Nernst Equation Electrochemical Calculator

Vary standard potential, temperature, concentration, and number of electrons to calculate electrode potential in real time. Intuitively experience electrochemistry fundamental to batteries, fuel cells, and corrosion engineering.

Half-Reaction Presets

Parameters

標準電極電位 E°
V
Temperature T
K
移動電子数 n
酸化体濃度 [Ox]
log
Slider is on log₁₀ scale
還元体濃度 [Red]
log
電極電位 E
—
V
反応商 Q
—
ネルンスト補正
— mV
RT/nF係数
— mV
方向
—
Conc
Theory & Key Formulas
$E = E^\circ - \dfrac{RT}{nF}\ln Q$

25°C近似：$E \approx E^\circ - \dfrac{0.0592}{n}\log_{10}Q$

$R=8.314$ J/(mol·K), $F=96485$ C/mol
$Q = \dfrac{[\text{Red}]}{[\text{Ox}]}$

🎓 Learn the Nernst Equation Through Conversation

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電池って習ったとき「銅と亜鉛を使ったダニエル電池は約1.1V」って覚えたんけど、なんで「約」なんか？ぴったり決まった値じゃないんか？
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鋭い疑問だ。そ 「1.1V」は標準電極電位 差（Cu°= +0.34V、Zn°= -0.76V）を使った理論値。でも実際は溶液中 Cu²⁺やZn²⁺ 濃度が1mol/L（標準状態）でない場合が多い。ネルンスト方程式はそ 補正をするんだ：$E = E^\circ - (RT/nF)\ln Q$。濃度が変わればVoltageも変わる。
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なるほど。じゃあ電池を使い続けてCu²⁺が減ってくるとVoltageが下がるんか？
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まさに。ダニエル電池 CathodeでCu²⁺が消費されるとQが大きくなり（還元体/酸化体 比が上がる）、ネルンスト補正項が大きくなって電位が下がる。電池が放電終止に近づくにつれてVoltageが徐々に落ちる はこ ためだ。Li-ion battery 放電曲線にも同じ原理が効いている。
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Temperatureでも変わるって聞きましたが、寒い日に車 Batteryが弱くなる はこれが理由か？
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それは複合的な原因があって、ネルンスト効果もあるけど主因は反応Velocity 低下（アレニウス則）と電解液粘度 上昇だ。低温だとIon 移動が遅くなり内部抵抗が上がる。一方、ネルンスト方程式 RT/nF 項はTemperatureに比例するfrom 、低温では濃度変化による電位変動が少し小さくなる側面もある。
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pH計ってGlass電極を使うやつよね。あれもネルンスト方程式で動いてるんか？
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そ とおり！H⁺/H₂ 半電池：$E = E^\circ - (0.0592/1)\log_{10}[H^+] = E^\circ + 0.0592 \times pH$。つまりpHが1上がるごとに電位が59.2mV変化する（25°C 場合）。Glass電極はこ 原理を使ってH⁺ 活量を電位として読み取る。pH計 校正をする はTemperatureが変わるとこ 係数（Nernst slope）が変わるfrom だよ。
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CAEとはどんな関係があるんか？
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腐食工学で直結する。配管や構造物 電気化学腐食をSimulationするとき、金属表面 電位分布（Laplace方程式）とネルンスト方程式を組み合わせて、どこが腐食しやすいかを予測する。また燃料電池（SOFC/PEFC CFD解析）でも電極電位 局所分布計算にネルンスト方程式が組み込まれている。

Frequently Asked Questions

What is the Nernst equation?
It is an equation that describes how the electrode potential of an electrochemical cell changes with the activity (concentration) of reactants and products. It is expressed as $E = E^\circ - \frac{RT}{nF}\ln Q$, where R is the gas constant, T is the absolute temperature, n is the number of electrons transferred, F is the Faraday constant (96485 C/mol), and Q is the reaction quotient. Under standard conditions (all activities = 1), Q = 1, ln Q = 0, and E = E°.
Are activity and concentration the same thing?
In dilute solutions (≈0.1 mol/L or less), the activity coefficient γ ≈ 1, so activity ≈ molar concentration can be approximated. At higher concentrations, interactions between cations and anions become stronger, leading to γ < 1, so accurate calculations require Debye-Hückel theory or measured activity coefficients. For engineering estimates, concentration is often used as a substitute.
How is the Nernst equation used in fuel cells?
The theoretical potential of a hydrogen-oxygen fuel cell is about 1.23 V at 25°C, but it varies with actual operating temperature (80–1000°C) and partial pressures of reactants. For example, in an SOFC (solid oxide fuel cell) at 700°C, it is calculated as $E = 1.23 + (RT/4F)\ln(p_{H_2} \cdot p_{O_2}^{1/2}/p_{H_2O})$. In CFD simulations, local potential maps are computed from local gas concentration distributions within the electrode.
What is the role of the Nernst equation in corrosion engineering?
It is used to calculate the corrosion potential (mixed potential) and passivation conditions of metals. In Pourbaix diagrams, the two axes of solution pH and potential show the boundaries of 'corrosion, passivation, and immunity' regions. These are drawn by plotting the potential of each reaction, obtained from $E^\circ - (RT/nF)\ln Q$, as a function of pH. This is important for corrosion protection design of structures and cathodic protection design.
When can the approximation '0.0592/n × log Q' be used?
This is an approximation using $RT\ln(10)/F = 0.02569 \times 2.303 ≈ 0.05916$ V at 25°C (298 K). When the temperature deviates significantly from 25°C (e.g., SOFC operation at 700°C or battery operation at -10°C in winter), the equation $RT/(nF)$ with the actual temperature T (K) must be used. Recording and correcting the solution temperature is also important during experimental measurements.

What is Nernst Equation Simulator?

Nernst Equation Simulator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.

Physical Model & Key Equations

The simulator is based on the governing equations behind Nernst Equation Electrochemical Calculator. Understanding these equations is key to interpreting the results correctly.

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Each parameter in the equations corresponds to a slider in the control panel. Moving a slider changes the equation's solution in real time, helping you build a direct connection between mathematical expressions and physical behavior.

Real-World Applications

Engineering Design: The concepts behind Nernst Equation Electrochemical Calculator are applied across mechanical, structural, electrical, and fluid engineering disciplines. This tool provides a quick way to estimate design parameters and sensitivity before committing to full CAE analysis.

Education & Research: Widely used in engineering curricula to connect theory with numerical computation. Also serves as a first-pass validation tool in research settings.

CAE Workflow Integration: Before running finite element (FEM) or computational fluid dynamics (CFD) simulations, engineers use simplified models like this to establish physical scale, identify dominant parameters, and define realistic boundary conditions.

Common Misconceptions and Points of Caution

Model assumptions: The mathematical model used here relies on simplifying assumptions such as linearity, homogeneity, and isotropy. Always verify that your real system satisfies these assumptions before applying results directly to design decisions.

Units and scale: Many calculation errors arise from unit conversion mistakes or order-of-magnitude errors. Pay close attention to the units shown next to each parameter input.

Validating results: Always sanity-check simulator output against physical intuition or hand calculations. If a result seems unexpected, review your input parameters or verify with an independent method.